Finally, we look at a notion of minimality related to the notion of primality.
We recall that a binary relational structure is prime (or indecomposable) if it has no nontrivial modules (see the definition in Section ). A hereditary class \(\mathfrak {C}\)  of finite binary structures is minimal prime if it contains infinitely many prime structures and every proper hereditary subclass has only finitely many prime structures. This notion appears in the thesis of D. Oudrar [1]}, where it is shown that a hereditary class which is minimal prime is an age (see Theorem REF ) and several examples are studied (see Chapter 6 of [1]}).
